Problem: Rewrite as a simplified fraction. ${3.\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 36.6666...\\ 1x &= 3.6666...\end{align*}}$ Subtracting the two equations, we have: ${9x = 33}$ ${x = \dfrac{33}{9}} $ ${x = \dfrac{11}{3}} \text{or} {3 \dfrac{2}{3}}$